Is it part of Rampant, Fixed, but I see no option to change the value? Biters constantly set up new bases one chunk away from my outposts, I find that a bit too close really.

Not certainly in that way. In siege mode, biters look for areas close to the base, but where turrets cannot kill them. They are quite capable of leaking through the perimeter if it has a couple of tiles of an unprotected passage.
But they will settle no closer than one chunk from the player's buildings.

However, I like the idea of putting the limiter in the settings

One chunk is super very close, are we talking of 32 'mini tiles' or more than that? Because I had to clear like 6 bases which were 60 tiles or so from my outposts. Perhaps they were sieges indeed! It has been tense...

It's 32-64 tiles away. Or further, if they are constantly killed there.

In fact, it is enough to kill these bases a couple of times so that they become afraid to settle there. Also, the idea of the siege was precisely to move the player perimeter as close as possible and push him out of the defense line.

But I know that a lot of people don't like biters firing at turrets with impunity.

Regarding the timing - this should not be expected in the next week

I think this is fine, I like the siege idea, I just thought they would encroach constantly too close. Plus if they can 'fear' losing a base in the same spot, this is very interesting, behavior-wise. Congrats btw, your improved AI is more interesting than the Rampant one.